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    Spherical coverage verification

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    1109.2361v1.pdf
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    Genre
    Journal Article
    Date
    2012-06-01
    Author
    Petković, MD
    Pokrajac, D
    Latecki, LJ
    Subject
    Geometrical algorithms
    Quadratic programming
    Hypersphere
    Coverage
    Hypercaps
    Permanent link to this record
    http://hdl.handle.net/20.500.12613/6001
    
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    DOI
    10.1016/j.amc.2012.03.014
    Abstract
    We consider the problem of covering hypersphere by a set of spherical hypercaps. This sort of problem has numerous practical applications such as error correcting codes and reverse k-nearest neighbor problem. Using the reduction of non-degenerated concave quadratic programming (QP) problem, we demonstrate that spherical coverage verification is NP hard. We propose a recursive algorithm based on reducing the problem to several lower dimension subproblems. We test the performance of the proposed algorithm on a number of generated constellations. We demonstrate that the proposed algorithm, in spite of its exponential worst-case complexity, is applicable in practice. In contrast, our results indicate that spherical coverage verification using QP solvers that utilize heuristics, due to numerical instability, may produce false positives. © 2012 Elsevier Inc. All rights reserved.
    Citation to related work
    Elsevier BV
    Has part
    Applied Mathematics and Computation
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    ae974a485f413a2113503eed53cd6c53
    http://dx.doi.org/10.34944/dspace/5983
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